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Find the area of the triangle: Round to the nearest tenth: a 18.2 b 17.1 12.3
Find the area of the triangle QRS A) 90 cmB) 80 cmC) 110 cmD) 55 cm E) 45 cm So PQ^2 = QR ^2 + PR^2• Let us take QR as the base here, because we have a right angled triangle involved in it, and the calculation of QR can be based on Pythagoras theorem. • We already have the values of PQ and PR values, so let’s use them to get the value of QR.132 = QR ^2 + 52169 = QR^2+ 25Subtract 25 on both sides 169-25 = QR ^2144 = QR^212 = QR QR = 12 cm • Therefore, the base of triangle QRS = 12 cm. We now need to find the height of the triangle so that we can find the area of it. Here, the height will be the altitude drawn from the vertex S to QR. • First we draw a perpendicular line from S to QR. Imagining the point of this line on QR as A, we then can see a square formed with points SAQT, with SQ as diagonal as shown in the figure. Therefore, as the opposite sides of a square are equal, the length of TQ is equal to the length of SA.TQ^2 + TS ^2 = QS^2TQ^2 + 82 = 172 TQ^2 + 64 = 289 Subtracting 64 on both sides TQ ^2 = 289-64TQ^2 = 225 Applying squaring on both sides TQ = 15So the length of TQ = 15 cmTherefore SA = 15 cmHence the altitude is 15 cm• Now we have the base and height, So we need to find the area of the triangle and we will reach the target• As Area = ½* base * HeightArea = ½* QR * SAArea = ½* 12 cm * 15 cmArea = 90 cm^2Therefore the area of triangle QRS = 90 cm ^2• By using Pythagoras theorem we have found the area of the triangle QRS As seen here, we have a mix of topics viz., square and right angled triangle.So the Answer will be Option A (90 cm). Disclaimer: The articles provided by GoGMAT are for informational purposes only and cannot be copied or redistributed without the written permission by GoGMAT. F1GMAT publishes guest posts by authors from all over the world. We do not accept any responsibility or liability for the information contained in the article or claims of copyright violation. However, we take immediate action when any copyright violations are reported. Report copyright violation |