Question

Calculate the length of AB. Round to the nearest tenth.

Answer 1

AB =10.06 ≈10.1 units

Explanation:

To answer this question we must draw a parallel line to the side AB, closing a triangle, so that we can visualize a triangle, and a square.

1) After drawing this red line. Since it's parallel we can assume it is the same length as AB. And as we have a Rectangular Triangle we can apply the Pythagoras Theorem.

The Parallelism assure us that the segment to the left below the red line measures the same if the angle is the same, namely 90º.

`10.5^(2)=3^(2)+h^(2)   \\ 110.25=9+h^(2) \\ 110.25-9=9+h^(2) -9\\ 101.25= h^(2)\\ h=√(101.25)\\  h=10.06 u`

Since h=AB Therefore AB=10.06 units

Answer 2

AB = 10.06 cm

Explanation:

Consider the given figure,

We have to find the length of side AB.

Lets rename the figure first, ABCD forms a rectangle. So , CB = DA = 12 cm

Also, EA = ED +DA ⇒ 15 = ED + 12 ⇒ ED = 15 - 12 ⇒ ED = 3 cm

Pythagoras theorem states that in a right triangle the sum of square of base and perpendicular is equal to square of hypotenuse.

Using, Pythagoras Theorem on Δ EDC,

`(EC)^2=(ED)^2+(DC)^2`

ED = 3 cm , EC = 10.5, Substitute, we get,

`\Rightarrow (10.5)^2=(3)^2+(DC)^2`

Solve for DC, we get,

`\Rightarrow 110.25=9+(DC)^2`

`\Rightarrow 110.25-9=(DC)^2`

`\Rightarrow (DC)^2=101.25`

`\Rightarrow DC=√(101.25)`

`\Rightarrow DC=10.06`

Since, ABCD is a rectangle. Thus, DC = AB

Hence, AB = 10.06 cm