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NeX [460]
4 years ago
11

If the height of the parallelogram shown is increased by 1 cm and the base is increased by 2 cm, what is the area of the new par

allelogram? A parallelogram with a base of 9 centimeters and a height of 4 centimeters. 28 cm2 39 cm2 55 cm2 60 cm2
Mathematics
1 answer:
Anni [7]4 years ago
7 0

Answer:

Area = 55 cm2

Step-by-step explanation:

It the base of the parallelogram was 9 centimeters and increased by 2, the new base has 9 + 2 = 11 centimeters.

It the height of the parallelogram was 4 centimeters and increased by 1, the new base has 4 + 1 = 5 centimeters.

Now, we can calculate the area of the parallelogram using the formula:

A = b * h

Where A is the area, b is the base and h is the height. So:

A = 11 * 5 = 55 cm2

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Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

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Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

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Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

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Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

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