Question

in trapezul MATE avem MA||TE, MA=40 cm, ET=15 cm, EM=15 cm, TA=20 cm. Calculati:a) inaltimea trapezului; b) aria si perimetrul trapezului; c) lungimea segmentului MT. Va rog urgent!!​

Answer 1

Răspuns:

A) h=12cm

B) [MT]=12√5 CM

Explicație pas cu pas:

verziatasamente

Answer 2

$\it Fie\ TF||EM \Rightarrow\Delta TFA -dreptunghic\ \^{i}n\ T,\ (15,\ 20,\ 25)-triplet\ pitagoreic.$

$\it\ h_{trapez}=h_{\Delta TFA}=\dfrac{15\cdot20}{25}=12\ cm\\ \\ \\ cos(TFA)=\dfrac{\ 15^{(5}}{25}=\dfrac{3}{5} \Rightarrow cos(TFM)=-\dfrac{3}{5}\\ \\ \\ MT^2=15^2+15^2-2\cdot15^2\cdot(-\dfrac{3}{5})=15^2(2+\dfrac{6}{5})=15\cdot15\cdot\dfrac{16}{5}=15\cdot3\cdot16=\\ \\ \\ = 5\cdot9\cdot16=5\cdot3^2\cdot4^2 \Rightarrow MT=12\sqrt5\ cm$