Area of a triangle PQR right-angled at Q is 60 cm² (Fig. 9.43). If the smallest side is 8cm long, find the length of the other two sides.
Solution:
Given, area of a triangle PQR right angled at Q is 60 cm²
The length of the smallest side is 8 cm
We have to find the length of the other two sides.
Area of triangle = 1/2 × base × height
Area of triangle PQR = 1/2 × 8 × QR
60 = 4 × QR
QR = 60/4
= 30/2
QR = 15 cm
By using Pythagoras theorem,
PR² = QR² + PQ²
PR² = (15)² + (8)²
PR² = 225 + 64
PR² = 289
Taking square root,
PR = 17 cm
Therefore, the length of the other two sides are 15 cm and 17 cm.
✦ Try This: A large square is made by arranging a small square surrounded by four congruent rectangles as shown in the given figure. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 90
Area of a triangle PQR right-angled at Q is 60 cm² (Fig. 9.43). If the smallest side is 8cm long, find the length of the other two sides.
Summary:
Area of a triangle PQR right-angled at Q is 60 cm² (Fig. 9.43). If the smallest side is 8cm long, the length of the other two sides are 15 cm and 17 cm
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