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Question Number 26528 by bbbbbb last updated on 26/Dec/17

f length of a rectangle is reduced by 5 umits and its breadth is increasesd 3 units then area of rectangle is reduced by 8 sq units if lenghth is reduced 3 units and breadth is increased by 2 units then area of rectangle will increased by 67 sq units . then find length and breadth of rectangle

$${f}\:{length}\:\:{of}\:{a}\:{rectangle}\:{is}\:{reduced}\:{by}\:\mathrm{5}\: \\ $$$${umits}\:{and}\:{its}\:{breadth}\:{is}\:{increasesd} \\ $$$$\mathrm{3}\:{units}\:{then}\:{area}\:{of}\:{rectangle}\:{is}\:{reduced} \\ $$$${by}\:\mathrm{8}\:{sq}\:{units}\:{if}\:{lenghth}\:{is}\:{reduced} \\ $$$$\mathrm{3}\:{units}\:{and}\:{breadth}\:{is}\:{increased}\:{by}\: \\ $$$$\mathrm{2}\:{units}\:{then}\:{area}\:{of}\:{rectangle} \\ $$$${will}\:{increased}\:{by}\:\mathrm{67}\:{sq}\:{units}\:.\: \\ $$$${then}\:{find}\:{length}\:{and}\:{breadth}\:{of}\:{rectangle} \\ $$

Answered by Rasheed.Sindhi last updated on 26/Dec/17

Let length & width of original rectangle are x & y respectively. xy−(x−5)(y+3)=8.......(i) (x−3)(y+2)−xy=67......(ii) (i)⇒xy−xy+15−3x+5y=8 3x−5y=7.........(iii) (ii)⇒xy+2x−3y−6−xy=67 2x−3y=73.......(iv) (iii)⇒6x−10y=14 (iv)⇒6x−9y=219 −y=−205 y=205 3x−5(205)=7 x=((7+1025)/3)=((1032)/3)=344 Length=344 , Breadth=205

$$\mathrm{Let}\:\mathrm{length}\:\&\:\mathrm{width}\:\mathrm{of}\:\mathrm{original}\:\mathrm{rectangle} \\ $$$$\mathrm{are}\:\mathrm{x}\:\&\:\mathrm{y}\:\mathrm{respectively}. \\ $$$$\mathrm{xy}−\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{y}+\mathrm{3}\right)=\mathrm{8}.......\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{y}+\mathrm{2}\right)−\mathrm{xy}=\mathrm{67}......\left(\mathrm{ii}\right) \\ $$$$\left(\mathrm{i}\right)\Rightarrow\mathrm{xy}−\mathrm{xy}+\mathrm{15}−\mathrm{3x}+\mathrm{5y}=\mathrm{8} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3x}−\mathrm{5y}=\mathrm{7}.........\left(\mathrm{iii}\right) \\ $$$$\left(\mathrm{ii}\right)\Rightarrow\mathrm{xy}+\mathrm{2x}−\mathrm{3y}−\mathrm{6}−\mathrm{xy}=\mathrm{67} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2x}−\mathrm{3y}=\mathrm{73}.......\left(\mathrm{iv}\right) \\ $$$$\:\left(\mathrm{iii}\right)\Rightarrow\mathrm{6x}−\mathrm{10y}=\mathrm{14} \\ $$$$\:\left(\mathrm{iv}\right)\Rightarrow\mathrm{6x}−\mathrm{9y}=\mathrm{219} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{y}=−\mathrm{205} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}=\mathrm{205} \\ $$$$\mathrm{3x}−\mathrm{5}\left(\mathrm{205}\right)=\mathrm{7} \\ $$$$\mathrm{x}=\frac{\mathrm{7}+\mathrm{1025}}{\mathrm{3}}=\frac{\mathrm{1032}}{\mathrm{3}}=\mathrm{344} \\ $$$$\mathrm{Length}=\mathrm{344}\:,\:\mathrm{Breadth}=\mathrm{205} \\ $$

Commented by bbbbbb last updated on 26/Dec/17

thank u

$${thank}\:{u} \\ $$

Commented by AHSoomro last updated on 26/Dec/17

Great Boss

$$\mathrm{Great}\:\mathrm{Boss} \\ $$

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