Question

In triangle LMN,LM=8cm,MN=6cm and LMN=90.X and Y are the midpoint of MN and LN retrospectively
Find YXN and YN

Answer 1

consider the above figure.

given,

• LMN = 90°

SO, ∆ LMN is a right angle triangle.

here,

• LM = 8 cm
• MN = 6 cm

by Pythagoras theorem,

$ln ^{2} = {lm}^{2} + {mn}^{2} \\ ln = \sqrt{ {lm}^{2} + {mn}^{2} } \\ ln = \sqrt{ {8}^{2} + {6}^{2} } \\ ln = \sqrt{64 + 36} \\ ln = \sqrt{100} \\ ln = 10$

now we get,

• LM = 8 cm
• MN = 6 cm
• LN = 10 cm

QUESTION: FIND YXN

we know,

in any triangle if the midpoint of any two sides are joined, the produced line segment is parallel to the third side.

here, midpoints of the two sides MN and LN are X and Y respectively. they are joined.

so we can state that,

XY।। LM

but,

LMN = 90°

so,

YXN = LMN = 90°

QUESTION: FIND YN

Here,

Y is the midpoint of LN.

so, YN = 1/2 of LN

that is,

$yn = \frac{1}{2} ln \\ yn = \frac{1}{2} \times 10 \\ yn = 5$

therefore,

YXN = 90°

YN = 5 cm