In the given diagram ABCK is a square an M - B - L (B is between M and L). If KL = 10 cm and MK = 24 cm, then what is the length of \(\overline {AB}\) in cm?

This question was previously asked in

Official Paper 8: OTET 2016 Paper 2 (Mathematics & Science)

Option 1 : \(7\frac{1}{{17}}\)

English Pedagogy - 1

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15 Questions
15 Marks
15 Mins

**Given:**

ABCK is a square

KL = 10 cm and MK = 24 cm

**Concept used:**

If the two triangles are similar then all the corresponding three sides of the given triangles are in the same proportion.

**Calculation:**

In ΔABM and ΔKLM

∠M = ∠M ----(Common angle)

∠ABM = ∠KLM ----(Corresponding angle)

∠MAB = ∠MKL ----(Corresponding angle)

So, ΔABM ~ ΔKLM by AAA property

Let the side of the square be x

MA = MK - AK = 24 - x

Now, By the property of similarity

MA/MK = AB/KL

⇒ (24 - x)/24 = x/10

⇒ 10(24 - x) = 24x

⇒ 240 - 10x = 24x

⇒ 34x = 240

⇒ x = 240/34

⇒ x = \(7\frac{1}{{17}}\)

**∴ The length of AB is \(7\frac{1}{{17}}\) cm**