A triangle with an area of 10 square meters has a base of 4 meters. A similar triangle has an area of 90 square meters. What is the height of the larger triangle?A triangle with an area of 10 square meters has a base of 4 meters. A similar triangle has an area of 90 square meters. What is the height of the larger triangle?

ANSWER

The height is 15 meters.

Area of smaller triangle is

[tex] = 10 {m}^{2} [/tex]



Area of larger triangle,

[tex] = 90 {m}^{2} [/tex]


Scale factor for the area is

[tex] {k}^{2} = \frac{90}{10} = 9[/tex]

This implies that,

[tex]k = \sqrt{9} = 3[/tex]


The length of the base of smaller triangle is

[tex] = 4[/tex]

This means that the length of the base of the larger triangle is


[tex] = 3 \times 4 = 12[/tex]

Area of the larger triangle is,

[tex]A= \frac{1}{2} \times b \times h[/tex]


[tex]90= \frac{1}{2} \times 12 \times h[/tex]

[tex]90= 6h[/tex]

[tex]h = \frac{90}{6} [/tex]

[tex]h = 15m[/tex]