Question

14.In the figure ABCD is a rectangle. AB= 5cm and AD= 4cm
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P
A
B
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i.
What is the area of AAEB?
ii.
Find the position of E, if AEB is an isosceles triangle?​

Answer 1

Step-by-step explanation:

Given: Here in the question it is given

(1) ABCD is a parallelogram,

(2) and

(3) , AB = 16 cm

(4) AE = 8cm

(5) CF = 10cm

To Find : AD =?

Calculation: We know that formula for calculating the

Therefore,

Area of paralleogram ABCD = DC × AE (Taking base as DC and Height as AE )

Area of paralleogram ABCD = AB × AE (AB = DC as opposite side of the parallelogram are equal)

Therefore,

Area of paralleogram ABCD = 16 × 8 ……(1)

Taking the base of Parallelogram ABCD as AD we get

Area of paralleogram ABCD = AD × CF (taking base as AD and height as CF)

Area of paralleogram ABCD = AD × 10 ……(2)

Since equation 1 and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.

Hence fro equation (1) and (2),

This means that,

Hence we get the result as

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Answer 2

Step-by-step explanation:

(1) AB = 6 --> clearly insufficient: BE can be 1 or 100.

(2) AE = 10 --> now, you should know one important property: for a given length of the hypotenuse a right triangle has the largest area when it's isosceles, so for our case area of ABE will be maximized when AB=BE. So, let's try what is the largest area of a right isosceles triangle with hypotenuse equal to 10. Finding legs: (where x=AB=BE) --> --> . Since it's the maximum area of ABE then the actual area cannot be more than 25. Sufficient.