Answer:
Area of the triangle(A) is given by:
\(A = \frac{1}{2}bh\) ....[1]
where,
b is the base and h is the height of the triangle.
As per the statement:
The area of a triangular block is 64 square inches.
⇒\(A= 64 in^2\)
It is given that: If the base of the triangle is twice the height
⇒\(b = 2h\) .....[2]
Substitute these in [1] we have;
\(64 = \frac{1}{2} \cdot (2h) \cdot h\)
⇒\(64 = h^2\)
or
\(h^2 = 64\)
⇒\(h = \sqrt{64} = 8\) inches.
Substitute h =8 in [2] we have;
\(b = 2(8) = 16\) in.
therefore, the base and height of the triangle are: 16 inches and 8 inches.
