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