A triangle has a base of 3 2/5 inches and an area of 5 1/10 square inches. Find the height of the triangle. Show your reasoning

Mathematics

1 answer:

photoshop1234 [79]2 years ago

6 0

Answer:

Step-by-step explanation:

Area if a traiangle =1/2 × base × height

5 1/10 = 1/2 ×3 2/5 ×h

Change mixed fractions to improper fractions

51/10= 1/2 ×17/5 ×h

51/10 = 17/10×h

Divide 51/10 by the coefficient of h

51/10÷17/5 = h

51/10 ×5/17 = h

3/2 = h

h =1 1/2 inchea

The height of the triangle 1 1/2 inches

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A cone and a triangular pyramid have a height of 9.3 m

Otrada [13]

Answer:

$x=17.1\ in$

Step-by-step explanation:

<u><em>The complete question is</em></u>

A cone and a triangular pyramid have a height of 9.3 m and their cross-sectional areas are equal at every level parallel to their respective bases. The radius of the base of the cone is 3 in and the other leg (not x) of the triangle base of the triangular pyramid is 3.3 in

What is the height, x, of the triangle base of the pyramid? Round to the nearest tenth

The picture of the question in the attached figure

we know that

If their cross-sectional areas are equal at every level parallel to their respective bases and the height is the same, then their volumes are equal

Equate the volume of the cone and the volume of the triangular pyramid

$\frac{1}{3}\pi r^{2}H=\frac{1}{3}[\frac{1}{2}(b)(h)H]$