There are 4 right triangles, the ratio of perpendicular sides being 3:4 in each. One more fact about each is given below. Find the length of the sides of each triangle. Then the area became 24 square metres
Answers
If the area of each triangle becomes 24 square metres then the length of the three sides of each triangle are 6 m, 8 m & 10 m.
Step-by-step explanation:
Step 1:
It is given that,
4 of the triangles are a right-angled triangle
The ratio of perpendicular sides of each = 3:4
So, let the length of the perpendicular sides of each triangle be “3x” and “4x”.
∴ Area of each right-angled triangle = ½ * base * height = ½ * [length of the two perpendicular sides]
⇒ 24 = ½ * 3x * 4x …… [∵ Area is given as 24 sq. meter]
⇒ 48 = 12x²
⇒ x² = 4
⇒ x = 2 m
∴ 3x = 3 × 2 = 6 m
And
4x = 4 × 2 = 8 m
Step 2:
We have calculated the length of the two perpendicular sides so, to find the length of the third side i.e., the hypotenuse in each of the triangles, we will apply the Pythagoras Theorem,
Hypotenuse = √[6² +8²] = √[36 + 64] = √[100] = 10 m
Thus, the length of the sides of the each of the triangles is 6 m, 8 m & 10 m.
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