Question

7. The sides of a right triangular park are in the ratio of 3 : 4, while its area is 486 sq m. Find the length of its hypotenuse.
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Answer 1

Given :

• The sides of a right triangular park are in the ratio of 3 : 4.
• Area of the right triangular park = 486 m².

To Find :

• Length of tha park's hypotenuse.

Solution :

According to the question :

Let, the sides of the park be 3x and 4x

Using Formula : Area of triangle = base × height

$\longrightarrow$ 486 = 1/2 × 3x × 4x

$\longrightarrow$ 486 = 1/2 × 12x²

$\longrightarrow$ 486 = 6x²

$\longrightarrow$ x² = 486/6

$\longrightarrow$ x² = 81

$\longrightarrow$ x = √81

$\longrightarrow$ x = 9

Reference of Figure :

$\setlength{\unitlength}{0.99cm}\begin{picture}(6, 4)\linethickness{0.26mm}\put(1,2){\line(1,0){2.8}}\put(3.9,4){\sf{36m}}\put(3.8,2){\line(0,2){4.5}}\put(2,1.7){\sf{27m}}\qbezier(1,2.05)(1.4,3)(3.8,6.5)\put(0.7,1.7){\bf{A}}\put(3.9,1.7){\bf{B}}\put(3.7,6.6){\bf{C}}\end{picture}$

$\longrightarrow$ AB = 3x = 3(9) = 27

$\longrightarrow$ BC = 4x = 4(9) = 36

Using Pythagoras Theorem : AC² = AB² + BC²

$\longrightarrow$ AC² = (27)² + (36)²

$\longrightarrow$ AC² = 729 + 1296

$\longrightarrow$ AC² = 2025

$\longrightarrow$ AC = √2025

$\longrightarrow$ AC = 45m

Hence, the hypotenuse of the park is 45m.