Explanation
Step 1: Find the base of the triangle
Let the base of the triangle be b meters and the height be h meters.
We are given:
The standard formula for the area of a triangle is:
Area=21×base×height
Substituting the given values into the formula:
180=21×b×24
Simplify the right side:
180=12×b
Solve for b:
b=12180
b=15 m
So, the base of the triangle is 15 m.
Step 2: Find the side of the square
Let the side length of the square be s meters.
According to the given condition, the side of the square is 3 less than the base of the triangle:
s=b−3
Substitute the value of b=15 m:
s=15−3
s=12 m
Step 3: Calculate the area of the square
The formula for the area of a square is:
Area of Square=s2
Substitute the value of s=12 m:
Area of Square=122=144 m2
Correct Answer:
(a) 144