Area of right-angle triangular park ABC is 84 m 2, AC is the long
| Area of right-angle triangular park ABC is 84 m2, AC is the longest side and AB is 17 m smaller than BC. If there is a point D on side AC such that AD is 10 m long, then what will be the area of triangle ABD?
A. 24.8 m<sup>2</sup>
B. 32.4 m<sup>2</sup>
C. 33.6 m<sup>2</sup>
D. 18 m<sup>2</sup>
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Given:
Formula Used:
Area of triangle = 1/2 × base × height
Calculation:
Let length of AB and BC be x and (x + 17) respectively
BP is perpendicular to AC
Area of ∆ABC = (1/2) × x × (x + 17) = 84
⇒ x(x + 17) = 168
⇒ x(x + 17) = 7 × (7 + 17)
⇒ x = 7
Now,
ΔABC
AC = √(x2 + (x + 17)2)
⇒ AC = √(72 + 242) = 25 m
Area of ∆ABC = (1/2) × 25 × BP = 84
⇒ BP = 6.72 m
Area of ∆ABD = (1/2) × AD × BP
⇒ Area of ∆ABD = (1/2) × 10 × 6.72 = 33.6 m2
∴ Area of ΔABD = 33.6 m2
