Legs (sides other than the hypotenuse) of a right triangle are of lengths 16cm and 8 cm. Find the length of the side of the largest square that can be inscribed in the triangle
Solution:
Given, the lengths of the sides of a right triangle (except hypotenuse) are 16 cm and 8 cm.
We have to find the length of the side of the largest square that can be inscribed in the triangle.
Let us consider a right triangle ABC with right angle at B.
Let PSRB be the largest square that can be inscribed in the triangle.
In the triangles ABC and APS, ∠A = ∠A (Common angle)
∠B = ∠P = 90°
AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.
By AAA criterion, the third angle will be equal.
So, ∠C = ∠S
Therefore, the two triangles are similar.
Let the side of the square PB = a cm
Given, AB = 16 cm
BC = 8 cm
Now, AP/AB = PS/BC
AP = AB - PB = 16 - a
Also, PB = PS = SR = RB = a cm.
16-a/16 = a/8
On cross multiplication,
8(16 - a) = 16a
16(8) - 8a = 16a
16(8) = 16a + 8a
Dividing by 8 on both sides,
16 = 2a + a
3a = 16
a = 16/3 cm
Therefore, the length of the side of the largest square that can be inscribed in the given triangle is 16/3 cm.
✦ Try This: Legs (sides other than the hypotenuse) of a right triangle are of lengths 4cm and 3 cm. Find the length of the side of the largest square that can be inscribed in the triangle
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Sample Problem 1
Legs (sides other than the hypotenuse) of a right triangle are of lengths 16cm and 8 cm. Find the length of the side of the largest square that can be inscribed in the triangle
Summary:
Legs (sides other than the hypotenuse) of a right triangle are of lengths 16cm and 8 cm. The length of the side of the largest square that can be inscribed in the triangle is 16/3 cm
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