The areas of two similar triangles are 121 cm^2 and 64 cm^2. A circle is inscribed in each triangle, and the radius of the circle inscribed in the larger triangle is 22 cm. Find the radius of the circle inscribed in the smaller triangle (in cm).

Question

Accepted Answer

16. Side ratio smaller : larger = √64/121 = 8/11, and an inradius is a length, so it scales like a side. Smaller inradius = 22 × 8/11 = 16 cm. Squaring the ratio a second time gives 22 × 64/121 11.6 cm, inverting it gives 22 × 11/8 = 30.25 cm, and 8 is merely a number from the ratio, not a radius.

The areas of two similar triangles are $121 cm^{2}$ and $64 cm^{2}$ . A circle is inscribed in each triangle, and the radius of the circle inscribed in the larger triangle is 22 cm.
Find the radius of the circle inscribed in the smaller triangle (in cm).

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More Class 10 Areas of Similar Triangles practice

The areas of two similar triangles are 121cm2 and 64cm2. A circle is inscribed in each triangle, and the radius of the circle inscribed in the larger triangle is 22 cm.Find the radius of the circle inscribed in the smaller triangle (in cm).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

The areas of two similar triangles are $121 cm^{2}$ and $64 cm^{2}$ . A circle is inscribed in each triangle, and the radius of the circle inscribed in the larger triangle is 22 cm.
Find the radius of the circle inscribed in the smaller triangle (in cm).