Question:
Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540cm. Find its area.
Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540cm. Find its area.
Updated On: Jun 9, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
Let the common ratio between the sides of the given triangle be x.
Therefore, the side of the triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
12x + 17x + 25x = 540 cm
\(⇒\) 54x = 540
x = \(\frac{540}{54}\)
x = 10 cm
The sides of the triangle:
12x = 12 × 10 = 120 cm,
17x = 17 × 10 = 170 cm,
25x = 25 × 10 = 250 cm
a = 120cm, b = 170 cm, c = 250 cm
Semi-perimeter(s) = \(\frac{540}{2}\) = 270 cm
By Heron’s formula,
Area of a triangle =\( \sqrt{\text{s(s - a)(s - b)(s - c)}}\)
\(= \sqrt{\text{270(270 - 120)(270 - 170)(270 - 250)}}\)
\(= \sqrt{\text{270 × 150 × 100 × 20}}\)
\(= \sqrt{81000000}\)
= 9000 cm2
Area of the triangle = 9000 cm2.
Therefore, the side of the triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
12x + 17x + 25x = 540 cm
\(⇒\) 54x = 540
x = \(\frac{540}{54}\)
x = 10 cm
The sides of the triangle:
12x = 12 × 10 = 120 cm,
17x = 17 × 10 = 170 cm,
25x = 25 × 10 = 250 cm
a = 120cm, b = 170 cm, c = 250 cm
Semi-perimeter(s) = \(\frac{540}{2}\) = 270 cm
By Heron’s formula,
Area of a triangle =\( \sqrt{\text{s(s - a)(s - b)(s - c)}}\)
\(= \sqrt{\text{270(270 - 120)(270 - 170)(270 - 250)}}\)
\(= \sqrt{\text{270 × 150 × 100 × 20}}\)
\(= \sqrt{81000000}\)
= 9000 cm2
Area of the triangle = 9000 cm2.
Was this answer helpful?
2
1
Top Questions on Area of a Triangle - by Heron’s Formula
- Consider the region \[ R = \left\{ (x, y): x \leq y \leq 9 - \frac{11}{3} x^2, x \geq 0 \right\}. \] The area of the largest rectangle of sides parallel to the coordinate axes and inscribed in \( R \) is:
- JEE Main - 2025
- Mathematics
- Area of a Triangle - by Heron’s Formula
Let \( A = \begin{bmatrix} \frac{1}{\sqrt{2}} & -2 \\ 0 & 1 \end{bmatrix} \) and \( P = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}, \theta > 0. \) If \( B = P A P^T \), \( C = P^T B P \), and the sum of the diagonal elements of \( C \) is \( \frac{m}{n} \), where gcd(m, n) = 1, then \( m + n \) is:
- JEE Main - 2025
- Mathematics
- Area of a Triangle - by Heron’s Formula
- The area of the region bounded by the curves \( x(1 + y^2) = 1 \) and \( y^2 = 2x \) is:
- JEE Main - 2025
- Mathematics
- Area of a Triangle - by Heron’s Formula
- Let A, B, C be three points in the xy-plane, whose position vectors are given by \[ \sqrt{3} \hat{i} + \hat{j}, \quad \hat{i} + \sqrt{3} \hat{j}, \quad \text{and} \quad a\hat{i} + (1-a) \hat{j} \] respectively with respect to the origin \( O \). If the distance of the point \( C \) from the line bisecting the angle between the vectors \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \) is \( \frac{9}{\sqrt{2}} \), then the sum of all possible values of \( a \) is:
- JEE Main - 2025
- Mathematics
- Area of a Triangle - by Heron’s Formula
- Let \( f: [0, 3] \to A \) be defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 7 \] and \( g: [0, \infty) \to B \) be defined by \[ g(x) = \frac{x}{x^{2025} + 1}. \] If both functions are onto and \[ S = \{ x \in \mathbb{Z} : x \in A \text{ or } x \in B \}, \] then \( n(S) \) is equal to:
- JEE Main - 2025
- Mathematics
- Area of a Triangle - by Heron’s Formula
View More Questions
Questions Asked in CBSE Class IX exam
- What are the main features of the mechanical teachers and the schoolrooms that Margie and Tommy have in the story?
- CBSE Class IX
- The fun they had
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play
- CBSE Class IX
- The fun they had
- Is there any difference between the two roads as the poet describes them:
(i) in stanzas two and three?
(ii) in the last two lines of the poem?- CBSE Class IX
- The fun they had
- Here is your diary entry when you visited Agra. Read the points and try to write a travelogue describing your visit to Agra and the Taj Mahal. You may add more details.
January 2003 — rise before dawn — take the Shatabdi Express at 6.15 a.m. from Delhi — meet a newly-married couple on train — talk about Himachal Pradesh — get off the train — enter the once-grand city, Agra — twisted alleys — traffic dense — rickshaws, cars, people — vendors selling religious artifacts, plastic toys, spices and sweets — go to the Taj Mahal — constructed entirely of white marble — magical quality — colour changes with varying of light and shadow — marble with gemstones inside — reflection of the Taj Mahal in the pond — school-children, tourists — tourist guides following people.- CBSE Class IX
- Kathmandu
- 1.The (site, cite) of the accident was (ghastly/ghostly).
2. Our college (principle/principal) is very strict.
3. I studied (continuously/continually) for eight hours.
4. The fog had an adverse (affect/effect) on the traffic.
5. Cezanne, the famous French painter, was a brilliant (artist/artiste).
6. The book that you gave me yesterday is an extraordinary (collage/college) of science fiction and mystery. 7. Our school will (host/hoist) an exhibition on cruelty to animals and wildlife conservation.
8. Screw the lid tightly onto the top of the bottle and (shake/shape) well before using the contents.- CBSE Class IX
- If I were you
View More Questions