The area of a rectangle is equal to area of a right-angle triangle. The breadth of the rectangle is 18 cm and the base of the triangle is 8 cm more than the length of the rectangle and height of the triangle is 3 cm more than length of the rectangle. Find length (in cm) of the rectangle (length > breadth)

Explanation

Information Given: The area of a rectangle is equal to area of a right-angle triangle. The breadth of the rectangle is 18 cm. The base of the triangle is 8 cm more than the length of the rectangle. The height of the triangle is 3 cm more than length of the rectangle. Formulas Used: Area of the triangle = 1/2 × Base × Height Area of the rectangle = Length × Breadth Basic Explanation: Let the length of the rectangle be L cm ATQ, 𝐿 × 18 = × (𝐿 + 8)(𝐿 + 3) 36𝐿 = 𝐿 + 11𝐿 + 24 𝐿2 − 25𝐿 + 24 = 0 𝐿2 − 24𝐿 − 𝐿 + 24 = 0 L = 24, 1 L = 24 Length of the rectangle = 24 cm