Question

The volume of the triangular block is 4 cubic inches. A triangular prism has a volume of 4 cubic inches. The right triangle bases have side lengths of x and a hypotenuse length of y. THe height of the prism is x. What is the approximate length of y? Round to the nearest tenth of an inch. 1. 4 in. 2. 0 in. 2. 8 in. 3. 5 in.

Answer 1

Answer:

2.8 INCHES

Step-by-step explanation:

Answer 2

The value of the hypotenuse y will be equal to y = 2.8 inches.

What is volume of prism?

The volume of the prism is equal to the product of the area of its base and the height of the prism.

$\rm V=Area \ of\ triangular \ base\times Height \ of \ prism$

The volume oif the prism is =4 cubic inches

Height of the prism = x inches

Base of the right angle isosceles triangle will be =x inches

The hypotenuse is given = y

Now

$\rm V=\dfrac{1}{2}\times Base\times Height \times height \ of \ prism$

$V=\dfrac{1}{2} \times x \times x \times x$

$x^3=8$

$x=2$

Now by pythagorus theorem

$y^2=h^2+b^2$

$y^2=x^2+x^2$

$y^2=2x^2=2\times 2^2$

$y=2\sqrt{2}=2.82$

Thus the value of the hypotenuse y will be equal to y = 2.8 inches.

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