Question

in triangle XYZ, YZ=4 cm and altitudes(heights) XM and YN are 5cm and 2.5cm respectively. find XZ​

Answer 1

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Answer 2

XZ = 8 cm

Step-by-step explanation:

In triangle XYZ

YZ=4 cm and altitudes XM and YN are 5cm and 2.5cm respectively.

then,

let the base be YZ and taking XM as a height

area of triangle = $\frac{1}{2} \times base \times height$

area = $\frac{1}{2}\times 4\times 5$

area = 10 cm²

now taking base = XZ  and height YN = 2.5 cm

using area = 10 cm²

then area of triangle = $\frac{1}{2} \times base \times height$

$10 = \frac{1}{2} \times XZ \times 2.5$

XZ = 8 cm

hence ,

XZ = 8 cm

#Learn more:

In a ∆XYZ , XM is perpendicular to YZ and YN to ZX . If XM and YN intersect at O , prove that XOY = 180 - Z

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